Week - 1 - Consistency of Units

Objective:

• To convert the given quantities(such as Mass, Length & Time etc) with the "SI" system of units into the required system of units(As mentioned in the question.
• LS-DYNA doesn't have a default system of units. To solve various problems associated with the different system of units, This consistency of units is performed. In order to find the conversion factors.
• To create a table at the end, for the obtained results.

Given quantities in SI units are:

MASS as "1kg"
LENGTH as "1m"
TIME as "1s"
FORCE as "1N"
STRESS as "1Pa"
ENERGY as "1Nm"
DENSITY as "1`(Kg)/m^3`"
YOUNG'S Modulus as "210GPa"
Velocity as "56.33`(KM)/H`"
GRAVITY as "9.8`m/s^2`"

The required system of units into which, The given quantities are to be converted are as follows:

Kg cm ms

Kg cm s

gm mm ms

kg m s

g cm s

g cm us

g mm s

ton mm s

slug ft s

kg mm s

g cm ms

kg mm ms

Usually, the quantities are classified into two types. They are:

1. Physical quantities(These are Independent quantities. These are also known as "Fundamental quantities").
2. Derived quantities(These are dependent quantities).

Some of the physical quantities with SI system of units are as follows:

Some of the derived quantities with SI system of units are as follows:

They are named as derived quantities because They are obtained with the help of two or more physical quantities.

Some basic conversions of the base quantities such as mass, length & time are as follows:

Mass; 1 Kilogram(Kg) = 1000grams(gm) = 0.001 ton = 0.068 slug. [1 ton = 1000kg]

Length; 1 Meter(M) = 100 centi-meters(cm) = 1000milli-meters(mm) = 3.28 ft.

Time; 1 seconds(S) = 1000 milli-seconds(ms) = `10^6`micro-seconds.

Some common terms of conversions, That is mostly seen are listed as follows:

1. Conversion of given quantities with SI units to kg cm ms:

Given mass => 1kg

Length => 1m = 100cm

Time => 1s = 1000ms

Force => 1N

The general formula for force derived from Newton's second law of motion is: Force(F) = Mass(M)*Acceleration(A)

Where Acceleration is the rate of change of velocity(With the SI units as: `m/(s^2)`

Then F = Mass(kg)*(Length(cm)/`Time^2`(`ms^2`)) = 1*(`100/(1000^2))` = `10^-4`kg*(`(cm)/(ms^2)`)

Therefore, the conversion factor is: `10^-4`

Stress =>1 Pascal(Pa) = 1 `N/m^2`

From the above derive unit for force => 1N = `10^-4`Kg*(`(cm)/(ms^2)`)

Then Stress = `10^-4`kg*(cm)/(ms^2)`/(10^2)^2`(`cm^2`) = `10^-8``(kg)/(cm*ms^2)` [Where 1m = 100 cm = 10^2 cm]

Therefore, the conversion factor is: `10^-8`

Energy => 1Nm

From the above derive unit for force => 1N = `10^-4`Kg*(`(cm)/(ms^2)`)

Then Energy = `10^-4`(Kg*(`(cm)/(ms^2)`))*`10^2`cm

= `10^-2``((kg*cm^2)/(ms^2))`

Therefore, the conversion factor is: `10^-2`

Density => 1`(kg)/m^3`

= `(1kg)/((10^2)^3 cm^3)`

= `(10^-6 )(kg)/(cm^3`

Therefore, the conversion factor is: `10^-6`

Youngs Modulus => 210 Giga-pascals(GPa)

= 210 *`10^9*(10^-8)(kg)/(cm*ms^2)`

= 210*10 = 2100 `(kg)/(cm*ms^2)`

Therefore, The conversion factor is: 10

Velocity => 56.33Kmph

1km = 1000m = 1000*`10^2`cm = `10^5`cm

1hr = 60(minutes)*60(seconds) = 3600 seconds = 3600*1000(milli seconds)

= 36*`10^5)`ms

1kmph = `(10^5)/(36*10^5)` = 0.0278 `(cm)/(ms)`

Therefore, 56.33*0.0278 = 1.566 `(cm)/(ms)`

Therefore, The conversion factor is: 0.0278 `(cm)/(ms)`

Gravity => 9.8m/s2

1m = 100cm

1s = `(10^3)^2``ms^2` = `10^6 ms^2`

Then, 9.8 `m/(s^2)`= `9.8*(100)/(10^6)``(cm)/(ms^2)`

= 9.8*`10^-4``(cm)/(ms^2)`

Therefore, The conversion factor is: `10^-4`

2. Conversion of given quantities with SI units to Kg cm s:

Given mass => 1kg

Length => 1m = 100cm

Time => 1s

Force => 1N

Force(F) = Mass(M)*Acceleration(A)

Where Acceleration is the rate of change of velocity(With the SI units as: `m/(s^2)`

Then F = Mass(kg)*(Length(cm)/`Time^2`(`s^2`)) = 1*(`100/(1^2))` = `10^2`kg*(`(cm)/(s^2)`)

Therefore, the conversion factor is: `10^2`

Stress =>1 Pascal(Pa) = 1 `N/m^2`

From the above derive unit for force => 1N = `10^2`Kg*(`(cm)/(s^2)`)

Then Stress = `10^2`kg*(cm)/(s^2)`/(10^2)^2`(`cm^2`) = `10^-2``(kg)/(cm*s^2)` [Where 1m = 100 cm = 10^2 cm]

Therefore, the conversion factor is: `10^-2`

Energy => 1Nm

From the above derive unit for force => 1N = `10^2`Kg*(`(cm)/(s^2)`)

Then Energy = `10^2`(Kg*(`(cm)/(s^2)`))*`10^2`cm

= `10^4``((kg*cm^2)/(s^2))`

Therefore, the conversion factor is: `10^4`

Density => 1`(kg)/m^3`

= `(1kg)/((10^2)^3 cm^3)`

= `(10^-6 )(kg)/(cm^3`

Therefore, the conversion factor is: `10^-6`

Youngs Modulus => 210 Giga-pascals(GPa)

= 210 *`10^9`*(10^-2)(kg)/(cm*s^2)`

= 210*`10^7` `(kg)/(cm*s^2)`

Therefore, The conversion factor is: `10^7`

Velocity => 56.33Kmph

1km = 1000m = 1000*`10^2`cm = `10^5`cm

1hr = 60(minutes)*60(seconds) = 3600 seconds

1kmph = `(10^5)/(3600)` = 27.78 `(cm)/(s)`

Therefore, 56.33*27.78 = 1564.84 `(cm)/(s)`

Therefore, The conversion factor is: 27.78 `(cm)/(ms)`

Gravity => 9.8m/s2

1m = 100cm

Then, 9.8 `m/(s^2)`= `9.8*(100)/(1^2)``(cm)/(s^2)`

= 9.8*`10^2``(cm)/(s^2)`

Therefore, The conversion factor is: `10^2`

3. Conversion of given quantities with SI units to gm mm ms:

Given mass => 1kg = 1000gm

Length => 1m = 100cm = 1000mm

Time => 1s = 1000ms

Force => 1N

Force(F) = Mass(M)*Acceleration(A)

Where Acceleration is the rate of change of velocity(With the SI units as: `m/(s^2)`

Then F = Mass(gm)*(Length(mm)/`Time^2`(`ms^2`)) = 1000*(`1000/(1000^2))` = `1`gm*(`(mm)/(ms^2)`)

Therefore, the conversion factor is: `1`

Stress =>1 Pascal(Pa) = 1 `N/m^2`

From the above derive unit for force => 1N = `1`gm*(`(mm)/(ms^2)`)

Then Stress = `1`gm*(mm)/(ms^2)`/(10^3)^2`(`mm^2`) = `10^-6``(gm)/(mm*ms^2)` [Where 1m = 100 cm = `10^2` cm = `10^3`mm]

Therefore, the conversion factor is: `10^-6`

Energy => 1Nm

From the above derive unit for force => 1N = 1 gm*(`(mm)/(ms^2)`)

Then Energy = 1 gm*(`(mm)/(ms^2)`)*`10^3`mm

= `10^3``((gm*mm^2)/(ms^2))`

Therefore, the conversion factor is: `10^3`

Density => 1`(kg)/m^3`

= `(1000gm)/((10^3)^3 mm^3)`

= `(10^-6 )(gm)/(mm^3)`

Therefore, the conversion factor is: `10^-6`

Youngs Modulus => 210 Giga-pascals(GPa)

= 210 *`10^9*(10^-6)(gm)/(mm*ms^2)`

= 210*`10^3` `(gm)/(mm*ms^2)`

Therefore, The conversion factor is: `10^3`

Velocity => 56.33Kmph

1km = 1000m = 1000*`10^3`mm = `10^6`mm

1hr = 60(minutes)*60(seconds) = 3600 seconds = 3600*1000(milli seconds)

= 36*`(10^5)`ms

1kmph = `(10^6)/(36*10^5)` = 2777.78 `(mm)/(ms)`

Therefore, 56.33*2777.78 = 156472.34`(mm)/(ms)`

Therefore, The conversion factor is: 2777.78 `(mm)/(ms)`

Gravity => 9.8m/s2

1m = 100cm =1000mm

1s = `(10^3)^2``ms^2` = `10^6 ms^2`

Then, 9.8 `m/(s^2)`= `9.8*(1000)/(10^6)``(mm)/(ms^2)`

= 9.8*`10^-3``(mm)/(ms^2)`

Therefore, The conversion factor is: `10^-3`

4. Conversion of given quantities with SI units to kg m s:

Given mass => 1kg

Length => 1m

Time => 1s

Force => 1N

Force(F) = Mass(M)*Acceleration(A)

Where Acceleration is the rate of change of velocity(With the SI units as: `m/(s^2)`

Then F = Mass(Kg)*(Length(m)/`Time^2`(`s^2`)) = 1*(`(1)/(`1^2`))` = `1`kg*(`(m)/(s^2)`)

Therefore, the conversion factor is: `1`

Stress =>1 Pascal(Pa) = 1 `N/m^2`

From the above derive unit for force => 1N = `1`kg*(`(m)/(s^2)`)

Then Stress = `1`kg*(m)/(s^2)`/(1)^2`(`m^2`) = `1``(kg)/(m*s^2)`

Therefore, the conversion factor is: `1`

Energy => 1Nm

From the above derive unit for force => 1N = `1`Kg*(`(m)/(s^2)`)

Then Energy = `1`(Kg*(`(m)/(s^2)`))*`1`m

= `1``((kg*m^2)/(s^2))`

Therefore, the conversion factor is: `1`

Density => 1`(kg)/m^3`

= `(1kg)/((1)^3 m^3)`

= `(1)(kg)/(m^3)`

Therefore, the conversion factor is: `1`

Youngs Modulus => 210 Giga-pascals(GPa)

= 210 *`10^9*(1)(kg)/(m*s^2)`

= 210*`10^9``(kg)/(m*s^2)`

Therefore, The conversion factor is: `10^9`

Velocity => 56.33Kmph

1km = 1000m

1hr = 60(minutes)*60(seconds) = 3600 seconds

1kmph = `(10^3)/(3600)` = 0.278 `(m)/(s)`

Therefore, 56.33*0.278 = 15.659 `(m)/(s)`

Therefore, The conversion factor is: 0.278 `(m)/(s)`

Gravity => 9.8m/s2 [Here, The units of the quantities are same as that of for SI units]

Therefore, The conversion factor is: `1`

5. Conversion of given quantities with SI units to g cm s:

Given mass => 1kg =1000gm

Length => 1m = 100cm

Time => 1s

Force => 1N

Force(F) = Mass(M)*Acceleration(A)

Where Acceleration is the rate of change of velocity(With the SI units as: `m/(s^2)`

Then F = Mass(gm)*(Length(cm)/`Time^2`(`s^2`)) = (1000)*(`100/(1^2))` = `10^5`gm*(`(cm)/(s^2)`)

Therefore, the conversion factor is: `10^5`

Stress =>1 Pascal(Pa) = 1 `N/m^2`

From the above derive unit for force => 1N = `10^5`gm*(`(cm)/(s^2)`)

Then Stress = `10^5`gm*(cm)/(s^2)`/(10^2)^2`(`cm^2`) = `10``(gm)/(cm*s^2)` [Where 1m = 100 cm = 10^2 cm]

Therefore, the conversion factor is: `10`

Energy => 1Nm

From the above derive unit for force => 1N = `10^5`gm*(`(cm)/(s^2)`)

Then Energy = `10^5`(gm*(`(cm)/(s^2)`))*`10^2`cm

= `10^7``((gm*cm^2)/(s^2))`

Therefore, the conversion factor is: `10^7`

Density => 1`(kg)/m^3`

= `(1000gm)/((10^2)^3 cm^3)`

= `(10^-3 )(gm)/(cm^3)`

Therefore, the conversion factor is: `10^-3`

Youngs Modulus => 210 Giga-pascals(GPa)

= 210 *`10^9*(10)(gm)/(cm*s^2)`

= 210*`10^10``(gm)/(cm*s^2)`

Therefore, The conversion factor is: `10^10`

Velocity => 56.33Kmph

1km = 1000m = 1000*`10^2`cm = `10^5`cm

1hr = 60(minutes)*60(seconds) = 3600 seconds

1kmph = `(10^5)/(3600)` = 27.78 `(cm)/(s)`

Therefore, 56.33*0.0278 = 1564.85 `(cm)/(s)`

Therefore, The conversion factor is: 27.78`(cm)/(s)`

Gravity => 9.8m/s2

1m = 100cm

Then, 9.8 `m/(s^2)`= `9.8*(100)/(`1^2`)``(cm)/(s^2)`

= 9.8*`10^2``(cm)/(s^2)`

Therefore, The conversion factor is: `10^2`

6. Conversion of given quantities with SI units to g cm `mu`s:

Given mass => 1kg = 1000gm

Length => 1m = 100cm

Time => 1s = `10^6``mu`s [Where, 1`mu`=`10^-6`]

Force => 1N

Force(F) = Mass(M)*Acceleration(A)

Where Acceleration is the rate of change of velocity(With the SI units as: `m/(s^2)`

Then F = Mass(gm)*(Length(cm)/`Time^2`(``mu`s^2`)) = 1000*(`(100)/`(10^6)^2`)` = `10^-7`gm*(`(cm)/(`mu`s^2)`)

Therefore, the conversion factor is: `10^-7`

Stress =>1 Pascal(Pa) = 1 `N/m^2`

From the above derive unit for force => 1N = `10^-7`gm*(`(cm)/(`mu`s^2)`)

Then Stress = `10^-7`gm*(cm)/(`mu`s^2)`/(10^2)^2`(`cm^2`) = `10^-11``(gm)/(cm*`mu`s^2)` [Where 1m = 100 cm = 10^2 cm]

Therefore, the conversion factor is: `10^-11`

Energy => 1Nm

From the above derive unit for force => 1N = `10^-7`gm*(`(cm)/(`mu`s^2)`)

Then Energy = `10^-7`(gm*(`(cm)/(`mu`s^2)`))*`10^2`cm

= `10^-5``((gm*cm^2)/(`mu`s^2))`

Therefore, the conversion factor is: `10^-5`

Density => 1`(kg)/m^3`

= `(1000gm)/((10^2)^3 cm^3)`

= `(10^-3)(gm)/(cm^3)`

Therefore, the conversion factor is: `10^-3`

Youngs Modulus => 210 Giga-pascals(GPa)

= 210 *`10^9*(10^-11)(gm)/(cm*`mu`s^2)`

= 210*`10^-2``(gm)/(cm*`mu`s^2)`

Therefore, The conversion factor is: `10^-2`

Velocity => 56.33Kmph

1km = 1000m = 1000*`10^2`cm = `10^5`cm

1hr = 60(minutes)*60(seconds) = 3600 seconds = 3600*`10^6`(micro seconds)

= 36*`(10^8)``mu`s

1kmph = `(10^5)/(36*10^8)` = 0.0278 *`10^-3``(cm)/(`mu`s)`

Therefore, 56.33*0.0278* `10^-3` = 0.00156`(cm)/(`mu`s)`

Therefore, The conversion factor is: 0.0278 *`10^-3``(cm)/(`mu`s)`

Gravity => 9.8m/s2

1m = 100cm

1s = `10^6``mu`s

Then, 9.8 `m/(s^2)`= `9.8*(100)/((10^6)^2)``(cm)/(`mu`s^2)`

= 9.8*`10^-10``(cm)/(`mu`s^2)`

Therefore, The conversion factor is: `10^-10`

7. Conversion of given quantities with SI units to g mm s:

Given mass => 1kg = 1000gm

Length => 1m = 1000mm

Time => 1s

Force => 1N

Force(F) = Mass(M)*Acceleration(A)

Where Acceleration is the rate of change of velocity(With the SI units as: `m/(s^2)`

Then F = Mass(gm)*(Length(mm)/`Time^2`(`s^2`)) = 1000*(`1000/(1^2))` = `10^6`gm*(`(mm)/(s^2)`)

Therefore, the conversion factor is: `10^6`

Stress =>1 Pascal(Pa) = 1 `N/m^2`

From the above derive unit for force => 1N = `10^6`gm*(`(mm)/(s^2)`)

Then Stress = `10^6`gm*(mm)/(s^2)`/(10^3)^2`(`mm^2`) = `1``(g)/(mm*s^2)`

Therefore, the conversion factor is: `1`

Energy => 1Nm

From the above derive unit for force => 1N = `10^6`gm*(`(mm)/(s^2)`)

Then Energy = `10^6`(gm*(`(mm)/(s^2)`))*`10^3`mm

= `10^9``((gm*mm^2)/(s^2))`

Therefore, the conversion factor is: `10^9`

Density => 1`(kg)/m^3`

= `(1000gm)/((10^3)^3 mm^3)`

= `(10^-6 )(gm)/(mm^3)`

Therefore, the conversion factor is: `10^-6`

Youngs Modulus => 210 Giga-pascals(GPa)

= 210 *`10^9*(1)(gm)/(mm*s^2)`

= 210*`10^9``(kg)/(cm*ms^2)`

Therefore, The conversion factor is: `10 ^9`

Velocity => 56.33Kmph

1km = 1000m = 1000*`10^3`mm = `10^6`mm

1hr = 60(minutes)*60(seconds) = 3600 seconds

1kmph = `(10^6)/(3600)` = 277.78 `(mm)/(s)`

Therefore, 56.33*277.78 = 15647.34 `(mm)/(s)`

Therefore, The conversion factor is: 277.78 `(mm)/(s)`

Gravity => 9.8m/s2

1m = 1000mm

Then, 9.8 `m/(s^2)`= `9.8*(1000)/(`1^2`)``(mm)/(s^2)`

= 9.8*`10^3``(mm)/(s^2)`

Therefore, The conversion factor is: `10^3`

8. Conversion of given quantities with SI units to ton mm s:

Given mass => 1kg = `10^-3`ton

Length => 1m = 1000mm

Time => 1s

Force => 1N

Force(F) = Mass(M)*Acceleration(A)

Where Acceleration is the rate of change of velocity(With the SI units as: `m/(s^2)`

Then F = Mass(ton)*(Length(mm)/`Time^2`(`s^2`)) = `10^-3`*(`1000/(1^2))` = `1`ton*(`(mm)/(s^2)`)

Therefore, the conversion factor is: `1`

Stress =>1 Pascal(Pa) = 1 `N/m^2`

From the above derive unit for force => 1N = `1`ton*(`(mm)/(s^2)`)

Then Stress = `1`ton*(`(mm)/(s^2)`)/((10^3)^2)`(`mm^2`) = `10^-6``(ton)/(mm*s^2)` [Where 1m = 100 cm = 10^2 cm]

Therefore, the conversion factor is: `10^-6`

Energy => 1Nm

From the above derive unit for force => 1N = `1`ton*(`(mm)/(s^2)`)

Then Energy = `1`ton*(`(mm)/(s^2)`)*`10^3`mm

= `10^3``((ton*mm^2)/(s^2))`

Therefore, the conversion factor is: `10^3`

Density => 1`(kg)/m^3`

= `(`10^-3`ton)/((10^3)^3 mm^3)`

= `(10^-12 )(ton)/(mm^3)`

Therefore, the conversion factor is: `10^-12`

Youngs Modulus => 210 Giga-pascals(GPa)

= 210 *`10^9`*(`10^-6`)(ton)/(mm*s^2)`

= 210*`10^3``(ton)/(mm*s^2)`

Therefore, The conversion factor is: `10^3`

Velocity => 56.33Kmph

1km = 1000m = 1000*`10^3`mm = `10^6`mm

1hr = 60(minutes)*60(seconds) = 3600 seconds

1kmph = `(10^6)/(3600)` = 277.78`(mm)/(s)`

Therefore, 56.33*277.78 = 15647.35 `(mm)/(s)`

Therefore, The conversion factor is: 277.78 `(mm)/(s)`

Gravity => 9.8m/s2

1m = 1000mm

Then, 9.8 `m/(s^2)`= `9.8*(1000)/(`1^2`)``(mm)/(s^2)`

= 9.8*`10^3``(mm)/(s^2)`

Therefore, The conversion factor is: `10^3`

9. Conversion of given quantities with SI units to slug ft s:

Given mass => 1kg = 0.068slug

Length => 1m = 3.28ft

Time => 1s

Force => 1N

Force(F) = Mass(M)*Acceleration(A)

Where Acceleration is the rate of change of velocity(With the SI units as: `m/(s^2)`

Then F = Mass(slug)*(Length(ft)/`Time^2`(`s^2`)) = 0.068*(`(3.28)/(1^2))` = `0.22304`slug*(`(ft)/(s^2)`)

Therefore, the conversion factor is: `0.22304`

Stress =>1 Pascal(Pa) = 1 `N/m^2`

From the above derive unit for force => 1N = `0.22304`slug*(`(ft)/(s^2)`)

Then Stress =`0.22304`slug*(`(ft)/(s^2)`)/(3.28)^2`(`ft^2`) = `0.0207``(slug)/(ft*s^2)`

Therefore, the conversion factor is: `0.0207`

Energy => 1Nm

From the above derive unit for force => 1N = `0.22304`slug*(`(ft)/(s^2)`)

Then Energy = `0.22304`slug*(`(ft)/(s^2)`)*`3.28`ft

= `0.732``((slug*ft^2)/(s^2))`

Therefore, the conversion factor is: `0.732`

Density => 1`(kg)/m^3`

= `(0.068slug)/`((3.28)^3)` ft^3)`

= `(2.4)(slug)/(ft^3)`

Therefore, the conversion factor is: `2.4`

Youngs Modulus => 210 Giga-pascals(GPa)

= 210 *`10^9*`0.0207``(slug)/(ft*s^2)`

= 210*207*`10^-5` `(slug)/(ft*s^2)` = 0.4347 `(slug)/(ft*s^2)`

Therefore, The conversion factor is: 207*`10^-5`

Velocity => 56.33Kmph

1km = 1000m = 1000*3.28 = 3280ft

1hr = 60(minutes)*60(seconds) = 3600 seconds

1kmph = `(3280)/(3600)` = 0.91 `(ft)/(s)`

Therefore, 56.33*0.0278 = 1.566 `(ft)/(s)`

Therefore, The conversion factor is: 0.91 `(ft)/(s)`

Gravity => 9.8m/s2

1m = 3.28ft

Then, 9.8 `m/(s^2)`= `9.8*(3.28)/(1^2)``(ft)/(s^2)`

= 32.14`(ft)/(s^2)`

Therefore, The conversion factor is: `3.28`

10. Conversion of given quantities with SI units to kg mm s:

Given mass => 1kg

Length => 1m = 1000mm

Time => 1s

Force => 1N

Force(F) = Mass(M)*Acceleration(A)

Where Acceleration is the rate of change of velocity(With the SI units as: `m/(s^2)`

Then F = Mass(kg)*(Length(mm)/`Time^2`(`s^2`)) = 1*(`1000/(1^2))` = `10^3`kg*(`(mm)/(s^2)`)

Therefore, the conversion factor is: `10^3`

Stress =>1 Pascal(Pa) = 1 `N/m^2`

From the above derive unit for force => 1N = `10^3`Kg*(`(mm)/(s^2)`)

Then Stress = `10^3`Kg*(`(mm)/(s^2)`)/(`10^3`)^2`(`mm^2`) = `10^-3``(kg)/(mm*s^2)`

Therefore, the conversion factor is: `10^-3`

Energy => 1Nm

From the above derive unit for force => 1N = `10^3`Kg*(`(mm)/(s^2)`)

Then Energy = `10^3`Kg*(`(mm)/(s^2)`)*`10^3`mm

= `10^6``((kg*mm^2)/(s^2))`

Therefore, the conversion factor is: `10^6`

Density => 1`(kg)/m^3`

= `(1kg)/((10^3)^3 mm^3)`

= `(`10^-9`)`(kg)/(mm^3)`

Therefore, the conversion factor is: `10^-9`

Youngs Modulus => 210 Giga-pascals(GPa)

= 210 *`10^9*(10^-3)(kg)/(mm*s^2)`

= 210*`10^6``(kg)/(mm*s^2)`

Therefore, The conversion factor is: `10^6`

Velocity => 56.33Kmph

1km = 1000m = 1000*`10^3`cm = `10^6`mm

1hr = 60(minutes)*60(seconds) = 3600 seconds

1kmph = `(10^6)/(3600)` = 277.78 `(mm)/(s)`

Therefore, 56.33*277.78 = 15647.35 `(mm)/(s)`

Therefore, The conversion factor is: 277.78 `(mm)/(s)`

Gravity => 9.8m/s2

9.8 `m/(s^2)`= `9.8*(1000)/(1^2)``(mm)/(s^2)`

= 9.8*`10^3``(mm)/(s^2)`

Therefore, The conversion factor is: `10^3`

11. Conversion of given quantities with SI units to g cm ms:

Given mass => 1kg = 1000gm

Length => 1m = 100cm

Time => 1s = 1000ms

Force => 1N

The general formula for force derived from Newton's second law of motion is: Force(F) = Mass(M)*Acceleration(A)

Where Acceleration is the rate of change of velocity(With the SI units as: `m/(s^2)`

Then F = Mass(gm)*(Length(cm)/`Time^2`(`ms^2`)) = 1000*(`100/(`1000^2`)` = `10^-1`gm*(`(cm)/(ms^2)`)

Therefore, the conversion factor is: `10^-1`

Stress =>1 Pascal(Pa) = 1 `N/m^2`

From the above derive unit for force => 1N = `10^-1`gm*(`(cm)/(ms^2)`)

Then Stress = `10^-1`gm*(`(cm)/(ms^2)`)/(10^2)^2`(`cm^2`) = `10^-5``(gm)/(cm*ms^2)`

Therefore, the conversion factor is: `10^-5`

Energy => 1Nm

From the above derive unit for force => 1N = `10^-1`gm*(`(cm)/(ms^2)`)

Then Energy = `10^-1`gm*(`(cm)/(ms^2)`)*`10^2`cm

= `10``((gm*cm^2)/(ms^2))`

Therefore, the conversion factor is: `10`

Density => 1`(kg)/m^3`

= `(1000gm)/((10^2)^3 cm^3)`

= `(10^-3 )(gm)/(cm^3)`

Therefore, the conversion factor is: `10^-3`

Youngs Modulus => 210 Giga-pascals(GPa)

= 210 *`10^9*(10^-5)(gm)/(cm*`ms^2`)`

= 210*`10^4``(gm)/(cm*`ms^2`)`

Therefore, The conversion factor is: `10^4`

Velocity => 56.33Kmph

1km = 1000m = 1000*`10^2`cm = `10^5`cm

1hr = 60(minutes)*60(seconds) = 3600 seconds = 3600*1000(milli seconds)

= 36*`(10^5)`ms

1kmph = `(10^5)/(36*10^5)` = 0.0278 `(cm)/(ms)`

Therefore, 56.33*0.0278 = 1.566 `(cm)/(ms)`

Therefore, The conversion factor is: 0.0278 `(cm)/(ms)`

Gravity => 9.8m/s2

1m = 100cm

1s = `(10^3)^2``ms^2` = `10^6 ms^2`

Then, 9.8 `m/(s^2)`= `9.8*(100)/(10^6)``(cm)/(ms^2)`

= 9.8*`10^-4``(cm)/(ms^2)`

Therefore, The conversion factor is: `10^-4`

12. Conversion of given quantities with SI units to kg mm ms:

Given mass => 1kg

Length => 1m = 1000mm

Time => 1s = 1000ms

Force => 1N

Force(F) = Mass(M)*Acceleration(A)

Where Acceleration is the rate of change of velocity(With the SI units as: `m/(s^2)`

Then F = Mass(kg)*(Length(mm)/`Time^2`(`ms^2`)) = 1*(`1000/(1000^2))` = `10^-3`kg*(`(mm)/(ms^2)`)

Therefore, the conversion factor is: `10^-3`

Stress =>1 Pascal(Pa) = 1 `N/m^2`

From the above derive unit for force => 1N = `10^-3`kg*(`(mm)/(ms^2)`)

Then Stress = `10^-3`kg*(`(mm)/(ms^2)`)/(10^3)^2`(`mm^2`) = `10^-9``(kg)/(mm*ms^2)`

Therefore, the conversion factor is: `10^-9`

Energy => 1Nm

From the above derive unit for force => 1N = `10^-3`kg*(`(cm)/(ms^2)`)

Then Energy = `10^-3`kg*(`(mm)/(ms^2)`)*`10^3`mm

= `1``((kg*mm^2)/(ms^2))`

Therefore, the conversion factor is: `1`

Density => 1`(kg)/m^3`

= `(1kg)/((`10^3`)^3 mm^3)`

= `10^-9``(kg)/(cm^3)`

Therefore, the conversion factor is: `10^-9`

Youngs Modulus => 210 Giga-pascals(GPa)

= 210 *`10^9*(10^-9)(kg)/(mm*ms^2)`

= 210`(kg)/(mm*ms^2)`

Therefore, The conversion factor is: 1

Velocity => 56.33Kmph

1km = 1000m = 1000*`10^3`cm = `10^6`mm

1hr = 60(minutes)*60(seconds) = 3600 seconds = 3600*1000(milli seconds)

= 36*`(10^5)`ms

1kmph = `(10^6)/(36*10^5)` = 0.278 `(mm)/(ms)`

Therefore, 56.33*0.278 = 15.66 `(mm)/(ms)`

Therefore, The conversion factor is: 0.278 `(mm)/(ms)`

Gravity => 9.8m/s2

1m = 1000mm

1s = `(10^3)^2``ms^2` = `10^6 ms^2`

Then, 9.8 `m/(s^2)`= `9.8*(1000)/(10^6)``(mm)/(ms^2)`

= 9.8*`10^-3``(mm)/(ms^2)`

Therefore, The conversion factor is: `10^-3`

Final table:

Conclusion:

• Converted the given quantities(such as Mass, Length & Time etc) with in the "SI" system of units into the required system of units(As mentioned in the question.
• Finally, Createda table at the end for the obtained results.